Middlesex made to suffer at Grace Road
They set a Leicestershire record for the fourth wicket, with Taylor not out on 206 and McDonald unbeaten on 176.
Leicestershire captain Matthew Hoggard declared with the total on 464-3, and Middlesex survived an awkward seven overs before the close to reach 19 without loss.
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Hide AdLeaders Glamorgan finished day two on 363-8 against Surrey in Cardiff, with openers Mark Cosgrove (82) and Gareth Rees (86) both impressing.
After a mid-innings wobble, Mark Wallace (58) and James Harris (49) put on 107 for the seventh wicket. Jade Dernbach was the most impressive of Surrey's bowlers, with 4-76.
Worcestershire were well set to overtake Gloucestershire's first-innings total as they reached 229-6 at the close in response to 245 all out.